Charmed meson masses and decay constants in the continuum limit from the tadpole improved clover ensembles

We present the determination of the charm quark mass, the masses, and decay constants of charmed mesons using thirteen <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math> flavor gauge ensembles at five different lattice spacings <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>a</c:mi><c:mo>∈</c:mo><c:mo stretchy="false">[</c:mo><c:mn>0.05</c:mn><c:mo>,</c:mo><c:mn>0.11</c:mn><c:mo stretchy="false">]</c:mo><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>fm</c:mi></c:math>, 8 pion masses <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:mi>π</g:mi></g:msub><g:mo>∈</g:mo><g:mo stretchy="false">(</g:mo><g:mn>130</g:mn><g:mo>,</g:mo><g:mn>360</g:mn><g:mo stretchy="false">)</g:mo><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>MeV</g:mi></g:math>, and several values of the strange quark mass, which allows us to do the chiral and continuum extrapolation. These ensembles are generated through the stout smeared clover fermion action and Symanzik gauge actions with the tadpole improvement. By absorbing the discretization errors into the masses and field normalization of the charm quark, we manage to suppress the discretization error of the charmed meson mass and all the S-wave open charmed meson decay constants to a few percent or even less at lattice spacing <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>a</k:mi><k:mo>∼</k:mo><k:mn>0.1</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>fm</k:mi></k:math>. Moreover, discretization errors for other quantities are also significantly reduced. The continuum extrapolated charm quark mass, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>m</m:mi><m:mi>c</m:mi></m:msub><m:mo stretchy="false">(</m:mo><m:msub><m:mi>m</m:mi><m:mi>c</m:mi></m:msub><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>1.2933</m:mn><m:mo stretchy="false">(</m:mo><m:mn>72</m:mn><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">(</m:mo><m:mn>95</m:mn><m:mo stretchy="false">)</m:mo><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>GeV</m:mi></m:math> in <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mover accent="true"><u:mi>MS</u:mi><u:mo stretchy="true">¯</u:mo></u:mover></u:math> scheme, is determined using QED-subtracted <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>D</y:mi><y:mi>s</y:mi></y:msub></y:math> meson mass and nonperturbative renormalization. Predictions of the open and close charm mesons using this charm quark mass agree with the experimental values at 0.1–0.5% level uncertainty. We obtained <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>D</ab:mi><ab:mrow><ab:mo stretchy="false">(</ab:mo><ab:mi>s</ab:mi><ab:mo stretchy="false">)</ab:mo></ab:mrow></ab:msub></ab:math> decay constants and also by far the most precise <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msubsup><eb:mi>D</eb:mi><eb:mrow><eb:mo stretchy="false">(</eb:mo><eb:mi>s</eb:mi><eb:mo stretchy="false">)</eb:mo></eb:mrow><eb:mo>*</eb:mo></eb:msubsup></eb:math> decay constants <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>f</ib:mi><ib:msup><ib:mi>D</ib:mi><ib:mo>*</ib:mo></ib:msup></ib:msub><ib:mo>=</ib:mo><ib:mn>0.2292</ib:mn><ib:mo stretchy="false">(</ib:mo><ib:mn>26</ib:mn><ib:mo stretchy="false">)</ib:mo><ib:mo stretchy="false">(</ib:mo><ib:mn>17</ib:mn><ib:mo stretchy="false">)</ib:mo><ib:mtext> </ib:mtext><ib:mtext> </ib:mtext><ib:mi>GeV</ib:mi></ib:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi>f</ob:mi><ob:msubsup><ob:mi>D</ob:mi><ob:mi>s</ob:mi><ob:mo>*</ob:mo></ob:msubsup></ob:msub><ob:mo>=</ob:mo><ob:mn>0.2691</ob:mn><ob:mo stretchy="false">(</ob:mo><ob:mn>30</ob:mn><ob:mo stretchy="false">)</ob:mo><ob:mo stretchy="false">(</ob:mo><ob:mn>03</ob:mn><ob:mo stretchy="false">)</ob:mo><ob:mtext> </ob:mtext><ob:mtext> </ob:mtext><ob:mi>GeV</ob:mi></ob:math>.